Nam H. Tran

Integrated conditional global optimisation for discrete fracture network modelling

This paper presents a methodology to simulate discrete fracture networks for naturally fractured reservoirs by combining statistical and spatial analyses, object-based modelling and conditional global optimisation. The methodology examines and utilises both continuum and discrete fracture information, such as spatial distribution of fracture density, statistical and geostatistical distributions of fracture size and orientation. The output is a network of discrete fractures, with their corresponding details of location, size and orientation. The methodology is illustrated by a case study on the surface fault system in New York region. The results show that it is able to produce discrete fracture network that match closely to the target fault map, even in the case where data are limited. The results show that it is also able to improve results of several recent fracture models, such as integrated stochastic simulations as well as grid-based simulations.

Practical Application of Hybrid Modelling to Naturally Fractured Reservoirs

Abstract This article presents application of a hybrid method for modelling discrete fracture network in an actual naturally fractured reservoir (NFRs) (Palm Valley, Australia). The hybrid method integrates features of geological, statistical, artificial intelligence, and conditional hierarchical stochastic simulation techniques. Both discrete and continuum fracture information could be utilized, such as statistical distributions of fracture orientations, spatial distributions of fracture density, and discrete multi-fractal dimensions. The final output is a 3D network model of discrete fractures, with their corresponding details of location, size, and orientation. The results show an improvement of the hybrid method over previous fracture models.

Fracture orientation characterization: Minimizing statistical modelling errors

Natural fractures are by nature extremely heterogeneous. Among the principal properties, fracture orientation is arguably the most diversified yet understudied. Fracture orientation contributes significantly to directional permeability and network connectivity. This paper proposes a multimodal circular statistical model to characterize fracture orientation data. First, the linear statistics is upgraded to circular statistics on modified orientation data to account for truncation and observational biases. Second, multimodal density functions are applied, in relations to the multiple stress directions and complex geological history. Third, while previous works represent dip and azimuth as separate properties, correlations between the two parameters exist and in some cases, are very strong. The introduction of circular representations, multimodal distributions and statistical correlations to characterization of fracture orientation is both significant and innovative. As shown in the case study, several disadvantages of previous studies, including observational and truncation biases, are omitted. The proposed characterization approach is also more versatile, data-driven, accurate and conclusive.

Combination of fuzzy ranking and simulated annealing to improve discrete fracture inversion

Mathematical and computational modelling of discrete fracture networks is critical for the exploration and development of natural resource reservoirs. Utilizing the concept of fuzzy memberships, this paper advances the fundamental understanding in fracture network inversion and presents a systematic procedure to solve the most important problem in global optimization (simulated annealing): objective function formulation. First, a comprehensive field study identifies all potential components of an objective function. The components are statistical, geostatistical, mathematical and spatial measurements of fracture properties (location, orientation and size). The characteristic measurements can be input in parametric or non-parametric, discrete or continuum forms. Next, sensitivity analysis and fuzzy logic are combined to rank the candidate components based on their effects on the final objective function value and optimization convergence. The process negates guess works in objective function formulation by automatic selection of highly ranked components and their corresponding weighting factors. A case study is applied to a surface DFN in New York. The derived discrete fracture network is representative of the field data.

Characterizing and Modelling of Fractured Reservoirs With Object-Oriented Global Optimization

Modelling of naturally fractured reservoirs is the first step to develop best scenarios for hydraulic fracture treatment, the design of an optimum production method and to evaluate reservoir potential. This paper reviews the state-of-the-art in current methods; hence, presents an integrated modelling methodology, utilizing object-based modelling, stochastic simulation and global optimization. Firstly, as an object-based model, each fracture is presented and treated as a discrete object. A stochastic simulation is carried out to generate an initial fracture network. An objective function is then formulated as the difference in statistics between the initial network and the target. Semi-variogram and other spatial statistical properties (cross variogram, multi-histogram mean and variogram distance) of fracture parameters are included so that the objective function is able to statistically describe representative field data. Subsequently, we use a global optimization algorithm to optimize the objective function. A case study is performed on an actual outcrop fault map to illustrate the proposed methodologys capacity. The results map the outcrop faults very closely.

Estimating Pressure Losses in Interconnected Fracture Systems: Integrated Tensor Approach

A significant number of petroleum reservoirs and almost all geothermal reservoirs are characterized by high in situ stress and fractures, and fractures act as major flow paths for fluids. An integrated tensor model is proposed to solve three tasks: characterization of a heterogeneous fracture network, simulation of fluid flow through a complex system for estimation of the grid-based permeability tensor, and unsteady-state fluid flow simulation for estimation of production and pressure losses. Deformation of the matrix and fractures are solved separately and used to compute their dynamic porosity and permeability. Finite-element methods and boundary element methods are used for numerical modeling. The results of this study show that the proposed model can overcome problems requiring excessive computational resources, flow interactions between the matrix and fracture, and the effect of matrix deformation on fluid flow. Results also show that the integrated tensor model serves as an efficient tool for predic...

Modelling of Type I fracture network: Objective function formulation by fuzzy sensitivity analysis

This paper advances the fundamental understanding in mathematical and computational modelling of discrete fracture networks (Type I). It presents a systematic procedure to solve the most important problem in modelling by global optimization - objective function formulation, which negates guesswork in objective function formulation by automatic selection of highly ranked components and their corresponding weighting factors. The procedure starts from real data to identify potential components of the objective function. The components are then ranked by fuzzy sensitivity analysis, based on their effects on the final objective function value and simulation convergence. The final fracture network inversion is subsequently realized and validated. Results of the study provide an explanation why previous methods such as stochastic simulations are not sufficiently reliable, compared to global optimization methods.